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<FONT color="green">001</FONT>    /*<a name="line.1"></a>
<FONT color="green">002</FONT>     * Licensed to the Apache Software Foundation (ASF) under one or more<a name="line.2"></a>
<FONT color="green">003</FONT>     * contributor license agreements.  See the NOTICE file distributed with<a name="line.3"></a>
<FONT color="green">004</FONT>     * this work for additional information regarding copyright ownership.<a name="line.4"></a>
<FONT color="green">005</FONT>     * The ASF licenses this file to You under the Apache License, Version 2.0<a name="line.5"></a>
<FONT color="green">006</FONT>     * (the "License"); you may not use this file except in compliance with<a name="line.6"></a>
<FONT color="green">007</FONT>     * the License.  You may obtain a copy of the License at<a name="line.7"></a>
<FONT color="green">008</FONT>     *<a name="line.8"></a>
<FONT color="green">009</FONT>     *      http://www.apache.org/licenses/LICENSE-2.0<a name="line.9"></a>
<FONT color="green">010</FONT>     *<a name="line.10"></a>
<FONT color="green">011</FONT>     * Unless required by applicable law or agreed to in writing, software<a name="line.11"></a>
<FONT color="green">012</FONT>     * distributed under the License is distributed on an "AS IS" BASIS,<a name="line.12"></a>
<FONT color="green">013</FONT>     * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.<a name="line.13"></a>
<FONT color="green">014</FONT>     * See the License for the specific language governing permissions and<a name="line.14"></a>
<FONT color="green">015</FONT>     * limitations under the License.<a name="line.15"></a>
<FONT color="green">016</FONT>     */<a name="line.16"></a>
<FONT color="green">017</FONT>    <a name="line.17"></a>
<FONT color="green">018</FONT>    package org.apache.commons.math3.analysis.function;<a name="line.18"></a>
<FONT color="green">019</FONT>    <a name="line.19"></a>
<FONT color="green">020</FONT>    import org.apache.commons.math3.analysis.FunctionUtils;<a name="line.20"></a>
<FONT color="green">021</FONT>    import org.apache.commons.math3.analysis.UnivariateFunction;<a name="line.21"></a>
<FONT color="green">022</FONT>    import org.apache.commons.math3.analysis.DifferentiableUnivariateFunction;<a name="line.22"></a>
<FONT color="green">023</FONT>    import org.apache.commons.math3.analysis.ParametricUnivariateFunction;<a name="line.23"></a>
<FONT color="green">024</FONT>    import org.apache.commons.math3.analysis.differentiation.DerivativeStructure;<a name="line.24"></a>
<FONT color="green">025</FONT>    import org.apache.commons.math3.analysis.differentiation.UnivariateDifferentiableFunction;<a name="line.25"></a>
<FONT color="green">026</FONT>    import org.apache.commons.math3.exception.NotStrictlyPositiveException;<a name="line.26"></a>
<FONT color="green">027</FONT>    import org.apache.commons.math3.exception.NullArgumentException;<a name="line.27"></a>
<FONT color="green">028</FONT>    import org.apache.commons.math3.exception.DimensionMismatchException;<a name="line.28"></a>
<FONT color="green">029</FONT>    import org.apache.commons.math3.util.FastMath;<a name="line.29"></a>
<FONT color="green">030</FONT>    <a name="line.30"></a>
<FONT color="green">031</FONT>    /**<a name="line.31"></a>
<FONT color="green">032</FONT>     * &lt;a href="http://en.wikipedia.org/wiki/Generalised_logistic_function"&gt;<a name="line.32"></a>
<FONT color="green">033</FONT>     *  Generalised logistic&lt;/a&gt; function.<a name="line.33"></a>
<FONT color="green">034</FONT>     *<a name="line.34"></a>
<FONT color="green">035</FONT>     * @since 3.0<a name="line.35"></a>
<FONT color="green">036</FONT>     * @version $Id: Logistic.java 1391927 2012-09-30 00:03:30Z erans $<a name="line.36"></a>
<FONT color="green">037</FONT>     */<a name="line.37"></a>
<FONT color="green">038</FONT>    public class Logistic implements UnivariateDifferentiableFunction, DifferentiableUnivariateFunction {<a name="line.38"></a>
<FONT color="green">039</FONT>        /** Lower asymptote. */<a name="line.39"></a>
<FONT color="green">040</FONT>        private final double a;<a name="line.40"></a>
<FONT color="green">041</FONT>        /** Upper asymptote. */<a name="line.41"></a>
<FONT color="green">042</FONT>        private final double k;<a name="line.42"></a>
<FONT color="green">043</FONT>        /** Growth rate. */<a name="line.43"></a>
<FONT color="green">044</FONT>        private final double b;<a name="line.44"></a>
<FONT color="green">045</FONT>        /** Parameter that affects near which asymptote maximum growth occurs. */<a name="line.45"></a>
<FONT color="green">046</FONT>        private final double oneOverN;<a name="line.46"></a>
<FONT color="green">047</FONT>        /** Parameter that affects the position of the curve along the ordinate axis. */<a name="line.47"></a>
<FONT color="green">048</FONT>        private final double q;<a name="line.48"></a>
<FONT color="green">049</FONT>        /** Abscissa of maximum growth. */<a name="line.49"></a>
<FONT color="green">050</FONT>        private final double m;<a name="line.50"></a>
<FONT color="green">051</FONT>    <a name="line.51"></a>
<FONT color="green">052</FONT>        /**<a name="line.52"></a>
<FONT color="green">053</FONT>         * @param k If {@code b &gt; 0}, value of the function for x going towards +&amp;infin;.<a name="line.53"></a>
<FONT color="green">054</FONT>         * If {@code b &lt; 0}, value of the function for x going towards -&amp;infin;.<a name="line.54"></a>
<FONT color="green">055</FONT>         * @param m Abscissa of maximum growth.<a name="line.55"></a>
<FONT color="green">056</FONT>         * @param b Growth rate.<a name="line.56"></a>
<FONT color="green">057</FONT>         * @param q Parameter that affects the position of the curve along the<a name="line.57"></a>
<FONT color="green">058</FONT>         * ordinate axis.<a name="line.58"></a>
<FONT color="green">059</FONT>         * @param a If {@code b &gt; 0}, value of the function for x going towards -&amp;infin;.<a name="line.59"></a>
<FONT color="green">060</FONT>         * If {@code b &lt; 0}, value of the function for x going towards +&amp;infin;.<a name="line.60"></a>
<FONT color="green">061</FONT>         * @param n Parameter that affects near which asymptote the maximum<a name="line.61"></a>
<FONT color="green">062</FONT>         * growth occurs.<a name="line.62"></a>
<FONT color="green">063</FONT>         * @throws NotStrictlyPositiveException if {@code n &lt;= 0}.<a name="line.63"></a>
<FONT color="green">064</FONT>         */<a name="line.64"></a>
<FONT color="green">065</FONT>        public Logistic(double k,<a name="line.65"></a>
<FONT color="green">066</FONT>                        double m,<a name="line.66"></a>
<FONT color="green">067</FONT>                        double b,<a name="line.67"></a>
<FONT color="green">068</FONT>                        double q,<a name="line.68"></a>
<FONT color="green">069</FONT>                        double a,<a name="line.69"></a>
<FONT color="green">070</FONT>                        double n)<a name="line.70"></a>
<FONT color="green">071</FONT>            throws NotStrictlyPositiveException {<a name="line.71"></a>
<FONT color="green">072</FONT>            if (n &lt;= 0) {<a name="line.72"></a>
<FONT color="green">073</FONT>                throw new NotStrictlyPositiveException(n);<a name="line.73"></a>
<FONT color="green">074</FONT>            }<a name="line.74"></a>
<FONT color="green">075</FONT>    <a name="line.75"></a>
<FONT color="green">076</FONT>            this.k = k;<a name="line.76"></a>
<FONT color="green">077</FONT>            this.m = m;<a name="line.77"></a>
<FONT color="green">078</FONT>            this.b = b;<a name="line.78"></a>
<FONT color="green">079</FONT>            this.q = q;<a name="line.79"></a>
<FONT color="green">080</FONT>            this.a = a;<a name="line.80"></a>
<FONT color="green">081</FONT>            oneOverN = 1 / n;<a name="line.81"></a>
<FONT color="green">082</FONT>        }<a name="line.82"></a>
<FONT color="green">083</FONT>    <a name="line.83"></a>
<FONT color="green">084</FONT>        /** {@inheritDoc} */<a name="line.84"></a>
<FONT color="green">085</FONT>        public double value(double x) {<a name="line.85"></a>
<FONT color="green">086</FONT>            return value(m - x, k, b, q, a, oneOverN);<a name="line.86"></a>
<FONT color="green">087</FONT>        }<a name="line.87"></a>
<FONT color="green">088</FONT>    <a name="line.88"></a>
<FONT color="green">089</FONT>        /** {@inheritDoc}<a name="line.89"></a>
<FONT color="green">090</FONT>         * @deprecated as of 3.1, replaced by {@link #value(DerivativeStructure)}<a name="line.90"></a>
<FONT color="green">091</FONT>         */<a name="line.91"></a>
<FONT color="green">092</FONT>        @Deprecated<a name="line.92"></a>
<FONT color="green">093</FONT>        public UnivariateFunction derivative() {<a name="line.93"></a>
<FONT color="green">094</FONT>            return FunctionUtils.toDifferentiableUnivariateFunction(this).derivative();<a name="line.94"></a>
<FONT color="green">095</FONT>        }<a name="line.95"></a>
<FONT color="green">096</FONT>    <a name="line.96"></a>
<FONT color="green">097</FONT>        /**<a name="line.97"></a>
<FONT color="green">098</FONT>         * Parametric function where the input array contains the parameters of<a name="line.98"></a>
<FONT color="green">099</FONT>         * the logit function, ordered as follows:<a name="line.99"></a>
<FONT color="green">100</FONT>         * &lt;ul&gt;<a name="line.100"></a>
<FONT color="green">101</FONT>         *  &lt;li&gt;Lower asymptote&lt;/li&gt;<a name="line.101"></a>
<FONT color="green">102</FONT>         *  &lt;li&gt;Higher asymptote&lt;/li&gt;<a name="line.102"></a>
<FONT color="green">103</FONT>         * &lt;/ul&gt;<a name="line.103"></a>
<FONT color="green">104</FONT>         */<a name="line.104"></a>
<FONT color="green">105</FONT>        public static class Parametric implements ParametricUnivariateFunction {<a name="line.105"></a>
<FONT color="green">106</FONT>            /**<a name="line.106"></a>
<FONT color="green">107</FONT>             * Computes the value of the sigmoid at {@code x}.<a name="line.107"></a>
<FONT color="green">108</FONT>             *<a name="line.108"></a>
<FONT color="green">109</FONT>             * @param x Value for which the function must be computed.<a name="line.109"></a>
<FONT color="green">110</FONT>             * @param param Values for {@code k}, {@code m}, {@code b}, {@code q},<a name="line.110"></a>
<FONT color="green">111</FONT>             * {@code a} and  {@code n}.<a name="line.111"></a>
<FONT color="green">112</FONT>             * @return the value of the function.<a name="line.112"></a>
<FONT color="green">113</FONT>             * @throws NullArgumentException if {@code param} is {@code null}.<a name="line.113"></a>
<FONT color="green">114</FONT>             * @throws DimensionMismatchException if the size of {@code param} is<a name="line.114"></a>
<FONT color="green">115</FONT>             * not 6.<a name="line.115"></a>
<FONT color="green">116</FONT>             * @throws NotStrictlyPositiveException if {@code param[5] &lt;= 0}.<a name="line.116"></a>
<FONT color="green">117</FONT>             */<a name="line.117"></a>
<FONT color="green">118</FONT>            public double value(double x, double ... param)<a name="line.118"></a>
<FONT color="green">119</FONT>                throws NullArgumentException,<a name="line.119"></a>
<FONT color="green">120</FONT>                       DimensionMismatchException,<a name="line.120"></a>
<FONT color="green">121</FONT>                       NotStrictlyPositiveException {<a name="line.121"></a>
<FONT color="green">122</FONT>                validateParameters(param);<a name="line.122"></a>
<FONT color="green">123</FONT>                return Logistic.value(param[1] - x, param[0],<a name="line.123"></a>
<FONT color="green">124</FONT>                                      param[2], param[3],<a name="line.124"></a>
<FONT color="green">125</FONT>                                      param[4], 1 / param[5]);<a name="line.125"></a>
<FONT color="green">126</FONT>            }<a name="line.126"></a>
<FONT color="green">127</FONT>    <a name="line.127"></a>
<FONT color="green">128</FONT>            /**<a name="line.128"></a>
<FONT color="green">129</FONT>             * Computes the value of the gradient at {@code x}.<a name="line.129"></a>
<FONT color="green">130</FONT>             * The components of the gradient vector are the partial<a name="line.130"></a>
<FONT color="green">131</FONT>             * derivatives of the function with respect to each of the<a name="line.131"></a>
<FONT color="green">132</FONT>             * &lt;em&gt;parameters&lt;/em&gt;.<a name="line.132"></a>
<FONT color="green">133</FONT>             *<a name="line.133"></a>
<FONT color="green">134</FONT>             * @param x Value at which the gradient must be computed.<a name="line.134"></a>
<FONT color="green">135</FONT>             * @param param Values for {@code k}, {@code m}, {@code b}, {@code q},<a name="line.135"></a>
<FONT color="green">136</FONT>             * {@code a} and  {@code n}.<a name="line.136"></a>
<FONT color="green">137</FONT>             * @return the gradient vector at {@code x}.<a name="line.137"></a>
<FONT color="green">138</FONT>             * @throws NullArgumentException if {@code param} is {@code null}.<a name="line.138"></a>
<FONT color="green">139</FONT>             * @throws DimensionMismatchException if the size of {@code param} is<a name="line.139"></a>
<FONT color="green">140</FONT>             * not 6.<a name="line.140"></a>
<FONT color="green">141</FONT>             * @throws NotStrictlyPositiveException if {@code param[5] &lt;= 0}.<a name="line.141"></a>
<FONT color="green">142</FONT>             */<a name="line.142"></a>
<FONT color="green">143</FONT>            public double[] gradient(double x, double ... param)<a name="line.143"></a>
<FONT color="green">144</FONT>                throws NullArgumentException,<a name="line.144"></a>
<FONT color="green">145</FONT>                       DimensionMismatchException,<a name="line.145"></a>
<FONT color="green">146</FONT>                       NotStrictlyPositiveException {<a name="line.146"></a>
<FONT color="green">147</FONT>                validateParameters(param);<a name="line.147"></a>
<FONT color="green">148</FONT>    <a name="line.148"></a>
<FONT color="green">149</FONT>                final double b = param[2];<a name="line.149"></a>
<FONT color="green">150</FONT>                final double q = param[3];<a name="line.150"></a>
<FONT color="green">151</FONT>    <a name="line.151"></a>
<FONT color="green">152</FONT>                final double mMinusX = param[1] - x;<a name="line.152"></a>
<FONT color="green">153</FONT>                final double oneOverN = 1 / param[5];<a name="line.153"></a>
<FONT color="green">154</FONT>                final double exp = FastMath.exp(b * mMinusX);<a name="line.154"></a>
<FONT color="green">155</FONT>                final double qExp = q * exp;<a name="line.155"></a>
<FONT color="green">156</FONT>                final double qExp1 = qExp + 1;<a name="line.156"></a>
<FONT color="green">157</FONT>                final double factor1 = (param[0] - param[4]) * oneOverN / FastMath.pow(qExp1, oneOverN);<a name="line.157"></a>
<FONT color="green">158</FONT>                final double factor2 = -factor1 / qExp1;<a name="line.158"></a>
<FONT color="green">159</FONT>    <a name="line.159"></a>
<FONT color="green">160</FONT>                // Components of the gradient.<a name="line.160"></a>
<FONT color="green">161</FONT>                final double gk = Logistic.value(mMinusX, 1, b, q, 0, oneOverN);<a name="line.161"></a>
<FONT color="green">162</FONT>                final double gm = factor2 * b * qExp;<a name="line.162"></a>
<FONT color="green">163</FONT>                final double gb = factor2 * mMinusX * qExp;<a name="line.163"></a>
<FONT color="green">164</FONT>                final double gq = factor2 * exp;<a name="line.164"></a>
<FONT color="green">165</FONT>                final double ga = Logistic.value(mMinusX, 0, b, q, 1, oneOverN);<a name="line.165"></a>
<FONT color="green">166</FONT>                final double gn = factor1 * Math.log(qExp1) * oneOverN;<a name="line.166"></a>
<FONT color="green">167</FONT>    <a name="line.167"></a>
<FONT color="green">168</FONT>                return new double[] { gk, gm, gb, gq, ga, gn };<a name="line.168"></a>
<FONT color="green">169</FONT>            }<a name="line.169"></a>
<FONT color="green">170</FONT>    <a name="line.170"></a>
<FONT color="green">171</FONT>            /**<a name="line.171"></a>
<FONT color="green">172</FONT>             * Validates parameters to ensure they are appropriate for the evaluation of<a name="line.172"></a>
<FONT color="green">173</FONT>             * the {@link #value(double,double[])} and {@link #gradient(double,double[])}<a name="line.173"></a>
<FONT color="green">174</FONT>             * methods.<a name="line.174"></a>
<FONT color="green">175</FONT>             *<a name="line.175"></a>
<FONT color="green">176</FONT>             * @param param Values for {@code k}, {@code m}, {@code b}, {@code q},<a name="line.176"></a>
<FONT color="green">177</FONT>             * {@code a} and {@code n}.<a name="line.177"></a>
<FONT color="green">178</FONT>             * @throws NullArgumentException if {@code param} is {@code null}.<a name="line.178"></a>
<FONT color="green">179</FONT>             * @throws DimensionMismatchException if the size of {@code param} is<a name="line.179"></a>
<FONT color="green">180</FONT>             * not 6.<a name="line.180"></a>
<FONT color="green">181</FONT>             * @throws NotStrictlyPositiveException if {@code param[5] &lt;= 0}.<a name="line.181"></a>
<FONT color="green">182</FONT>             */<a name="line.182"></a>
<FONT color="green">183</FONT>            private void validateParameters(double[] param)<a name="line.183"></a>
<FONT color="green">184</FONT>                throws NullArgumentException,<a name="line.184"></a>
<FONT color="green">185</FONT>                       DimensionMismatchException,<a name="line.185"></a>
<FONT color="green">186</FONT>                       NotStrictlyPositiveException {<a name="line.186"></a>
<FONT color="green">187</FONT>                if (param == null) {<a name="line.187"></a>
<FONT color="green">188</FONT>                    throw new NullArgumentException();<a name="line.188"></a>
<FONT color="green">189</FONT>                }<a name="line.189"></a>
<FONT color="green">190</FONT>                if (param.length != 6) {<a name="line.190"></a>
<FONT color="green">191</FONT>                    throw new DimensionMismatchException(param.length, 6);<a name="line.191"></a>
<FONT color="green">192</FONT>                }<a name="line.192"></a>
<FONT color="green">193</FONT>                if (param[5] &lt;= 0) {<a name="line.193"></a>
<FONT color="green">194</FONT>                    throw new NotStrictlyPositiveException(param[5]);<a name="line.194"></a>
<FONT color="green">195</FONT>                }<a name="line.195"></a>
<FONT color="green">196</FONT>            }<a name="line.196"></a>
<FONT color="green">197</FONT>        }<a name="line.197"></a>
<FONT color="green">198</FONT>    <a name="line.198"></a>
<FONT color="green">199</FONT>        /**<a name="line.199"></a>
<FONT color="green">200</FONT>         * @param mMinusX {@code m - x}.<a name="line.200"></a>
<FONT color="green">201</FONT>         * @param k {@code k}.<a name="line.201"></a>
<FONT color="green">202</FONT>         * @param b {@code b}.<a name="line.202"></a>
<FONT color="green">203</FONT>         * @param q {@code q}.<a name="line.203"></a>
<FONT color="green">204</FONT>         * @param a {@code a}.<a name="line.204"></a>
<FONT color="green">205</FONT>         * @param oneOverN {@code 1 / n}.<a name="line.205"></a>
<FONT color="green">206</FONT>         * @return the value of the function.<a name="line.206"></a>
<FONT color="green">207</FONT>         */<a name="line.207"></a>
<FONT color="green">208</FONT>        private static double value(double mMinusX,<a name="line.208"></a>
<FONT color="green">209</FONT>                                    double k,<a name="line.209"></a>
<FONT color="green">210</FONT>                                    double b,<a name="line.210"></a>
<FONT color="green">211</FONT>                                    double q,<a name="line.211"></a>
<FONT color="green">212</FONT>                                    double a,<a name="line.212"></a>
<FONT color="green">213</FONT>                                    double oneOverN) {<a name="line.213"></a>
<FONT color="green">214</FONT>            return a + (k - a) / FastMath.pow(1 + q * FastMath.exp(b * mMinusX), oneOverN);<a name="line.214"></a>
<FONT color="green">215</FONT>        }<a name="line.215"></a>
<FONT color="green">216</FONT>    <a name="line.216"></a>
<FONT color="green">217</FONT>        /** {@inheritDoc}<a name="line.217"></a>
<FONT color="green">218</FONT>         * @since 3.1<a name="line.218"></a>
<FONT color="green">219</FONT>         */<a name="line.219"></a>
<FONT color="green">220</FONT>        public DerivativeStructure value(final DerivativeStructure t) {<a name="line.220"></a>
<FONT color="green">221</FONT>            return t.negate().add(m).multiply(b).exp().multiply(q).add(1).pow(oneOverN).reciprocal().multiply(k - a).add(a);<a name="line.221"></a>
<FONT color="green">222</FONT>        }<a name="line.222"></a>
<FONT color="green">223</FONT>    <a name="line.223"></a>
<FONT color="green">224</FONT>    }<a name="line.224"></a>




























































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